The Traits of Quarternary Minimum-Energy Frames in Sobolev Space

摘要

The concept of a generalized quarternary multiresolution struccture (GQMS) of space is formulated. A class of multiple affine quarternary pseudo frames for subspaces of L~2(R~4) are introduced. The construction of a GQMS of Paley-Wiener subspaces of L~2(R~4) is studied. The sufficient condition for the existence of pyramid decomposition scheme is presented based on such a GQMS. A sort of affine quarternary frames are constructed by virtue of the pyramid decomsition scheme and Fourier transform. We show how to draw new orthonormal bases for space L~2(R~4) from these wavelet wraps.